Abstract

The temperature dependent optical parameters n and k of amorphous silicon deposited by electron beam evaporation were determined at the wavelength of 808 nm. This was achieved by fitting an optical model of the layer system to reflection values of a fs-laser beam. From n(T) and k(T) the absorption of a-Si layers as depending on thickness and temperature were calculated for this diode laser wavelength. By heating the layers to 600 °C the absorption can be increased by a factor of 4 as compared to room temperature, which allows for diode laser crystallization of layers down to 80 nm in thickness.

© 2012 OSA

1. Introduction

Coarse-grained multicrystalline silicon thin films on glass are of great interest for high efficiency thin film solar cells and for thin film transistors (TFTs) in flat panel displays. Usually multicrystalline silicon thin film solar cells are based on a seed layer [1] with the desired crystal structure which should be as thin as possible. The seed layer then is epitaxially thickened to several µm [24]. High quality seed layers and layers for TFTs with grain sizes exceeding 100 µm have been prepared from amorphous silicon (a-Si) films by cw laser crystallization via melting in the ms regime [5,6]. This melting time is short enough as not to jeopardize the glass substrate, and long enough for lateral crystal growth up to about 100 µm. TFTs prepared into these films showed a high field effect mobility of 690 Vs/cm2 [5]. Usually crystalline silicon layers for TFTs are crystallized by using short pulse (ns) lasers, e.g. excimer lasers. However, due to the short melting time, in this case grain sizes of only some µm result [7].

The main criterion for selecting an appropriate laser for crystallization is the emitted wavelength since the absorption of the thin silicon layer strongly depends on wavelength. The best choice would be a wavelength for which the absorption length is a bit shorter than the film thickness. If the absorption length is much larger than the film thickness, the laser light is coupled into the silicon layer very ineffectively. Then a rather high laser power is necessary to reach the melting temperature of silicon (1685 K), and the crystallization process gets unstable, for example due to overheating at strongly absorbing defects.

Due to the absorption properties of amorphous silicon, lasers emitting in the blue or green spectral range would be favorable. However, high power cw lasers in this wavelength range exhibit poor power efficiency. In contrast, high power diode lasers emitting in the near infrared (NIR, 800-1000 nm) are available with a power up to the kW range. Moreover, beam shaping for a line focus has been demonstrated [8]. Unfortunately, the absorption length of amorphous silicon in the NIR exceeds some micrometers, too large for a layer thickness in the range of some tens to hundreds of nm. However, at higher temperature the absorption of silicon strongly increases [9]. Consequently, near infrared diode laser crystallization of thin a-Si layers on glass substrates preheated to about 600 °C has been demonstrated, resulting in coarse grained silicon seed layers of thickness between several µm and down to about 150 nm useful for photovoltaic applications [6,1012]. The wavelength of the laser used was the shortest available high-power diode laser wavelength (808 nm with a bandwidth of some nm). Lasers with a longer wavelength, e.g. 960 nm, are not useful due to the very low silicon absorption even when preheated.

Besides the poor absorption of amorphous silicon in the NIR region, strong interference modulations of the absorption in the thin layers, as depending on the wavelength and the layer thickness, complicate the adjustment of optimal crystallization parameters.

For calculating the irradiation parameters useful for crystallization of a specific layer thickness, the temperature dependent optical parameters (refractive index n and extinction coefficient k) are required for the wavelength under consideration. Moreover, based on these data the interference modulation of the light absorption can be estimated as evolving during the heating process. From these data the minimum useful layer thickness may be determined.

A common method for measuring n and k of thin films is ellipsometry. However, for temperatures of some hundred degrees a considerable experimental effort is necessary [13]. In this paper we present the results of the temperature dependence of n and k up to nearly 600 °C as measured by a relatively simple reflectivity measurement. As an example we used amorphous silicon films deposited onto a glass substrate by electron beam evaporation (EBE). Furthermore we present estimates of the absorption up to more than 1000 °C, a temperature range useful for solid phase epitaxy of amorphous silicon.

2. Experimental

The optical parameters of an amorphous silicon layer can be determined from the transmission and reflection spectra if the coherence length, respectively the bandwidth, of the light source is in an appropriate relation to the film and substrate thicknesses. The coherence length of the light source should be large as compared to the optical film thickness and small as compared to the substrate thickness. Under these conditions the theoretical description of a “thin film” on a “thick substrate” applies with coherent superposition within the film and incoherent superposition within the substrate [14]. When measuring the temperature dependent optical parameters, strong temperature dependent modulations in the spectra resulting from the heated substrate easily can be eliminated under the “thin film on thick substrate” conditions. We used some hundred nm thick amorphous silicon layers deposited by electron beam evaporation on a 3.3 mm thick glass substrate (borosilicate glass - Schott Borofloat33). For these samples and for the spectral range from the visible region to the NIR the light source should have a spectral bandwidth larger than 200 pm and smaller than about 10 nm. After the deposition the samples were heated to 540 °C for several minutes in order to induce some structural relaxation processes within the amorphous phase [15]. After this treatment the samples are stable and do not change anymore after following heating cycles.

At room temperature the spectra were measured using a spectrometer with an integrating sphere (Perkin Elmer - Lambda900) from 700 nm up to 2000 nm with steps of 2 nm (2 nm bandwidth in the VIS, 5 nm bandwidth in the NIR). The large wavelength interval up to the NIR was chosen so as to estimate the film thickness and the dispersion of the optical constants n and k from the interference modulated spectra.

Substrate heating up to 600 °C was not possible inside the spectrometer. Instead, a tunable laser with an appropriate coherence length was applied as a light source for the measurement of the temperature dependent reflectivity. A home-made Ni-heater was used for heating. The sample was radiation heated 1 mm in front of a hot Ni plate. As a laser a mode-locked Ti:sapphire femtosecond(fs)-laser was used (Coherent, Mira900D, repetition rate 76 MHz, pulse length ~100 fs at 10 nm spectral bandwidth, beam diameter at sample 3 mm) which was tuned in the interesting wavelength range from 760 nm to 870 nm. This range covers the wavelength emitted by high power diode lasers useful for silicon crystallization, as described in the Introduction. The tuning range is large enough to follow the change of the interference modulated reflection spectra by heating the sample (e.g. displacement of a minimum in the spectrum). The laser wavelength was measured by a laser spectrometer (APE, PulseScope, resolution < 1nm) and was manually tuned in steps of about 5 nm. By adjusting the group velocity dispersion of the fs-laser, the bandwidth for each wavelength was set to 5 ( ± 1) nm, corresponding to a coherence length in air of 60 µm. This bandwidth is appropriate for the calculation model and allows for the intended spectral resolution.

The optical set up for the reflectivity measurement is shown in Fig. 1 . The beam was nearly perpendicular (angle of incidence < 2°) to the sample surface. The reflected intensity was measured by a thermal power sensor (Ophir, 3W) in a distance of about 1 m in order to sufficiently eliminate the thermal influence of the heater. The laser power was tuned by a half-wave plate in combination with a polarizer and was set to 100 mW. Additional heating of the substrate by the laser beam was negligible. By a second detector the power of the incoming beam was measured by out-coupling a part of the incoming beam by a beam splitter. For calibration (100% incoming power) the reflection detector was once set in front of the substrate.

 

Fig. 1 Optical set-up for the measurement of temperature dependent reflectivity (see text).

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3. Results

Spectra were measured at room temperature for a 480 nm and for a 520 nm thick amorphous silicon layer (see Fig. 2 for the 520 nm sample).

 

Fig. 2 Spectra of a 520 nm thick a-Si film measured by a spectrometer (dots mark every tenth of the measured wavelengths) and fitted spectra for reflection R (blue, dotted), transmission T (red, solid) and absorption A = 1-R-T (black, dash-dotted). The diameter of the points gives a good hint for the accuracy of measurement.

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The optical parameters n and k of amorphous silicon at room temperature were calculated for each sample from the spectrometer data (points in Fig. 2) by a fit procedure. We used a theoretical model for spectra of a thin absorbing film on an absorption free substrate given by [14].

In the wavelength region of interest above 700 nm the dispersion varies rather smoothly. The optical parameters of a-Si can be modeled in good approximation with only 5 parameters (a to e) according to

n(λ)=a(λb)2+ck(λ)=d(λe)2
where λ is the wavelength, n(λ) is the refractive index, and k(λ) is the extinction coefficient, related to the absorption coefficient α by α = 4π*k/λ. Fitting yielded the parameters
a=155000nm2,b=220nm,c=3.5,d=1180nm2,e=610nm.
The dispersion of n and k is shown in Fig. 3 . For the wavelength of 808 nm, the mean wavelength of the diode laser used for laser crystallization, the room temperature values are

 

Fig. 3 Dispersion of n and k of a-Si at room temperature.

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  • refractive index n0 = 3.95 ± 0.05
  • extinction coefficient k0 = 0.030 ± 0.004
  • absorption constant α0 = 4670 cm−1
  • absorption length labs = 2140 nm.

The absorption length is given by labs = 1/α0.

Reflection spectra of the same sample as used in Fig. 2, determined by fs-laser illumination, are shown in Fig. 4 for seven different temperatures (from 20 °C to 540 °C). By heating the sample the refractive index of the a-Si film increases so that the interference minima and maxima shift to longer wavelengths. The extinction coefficient increases as well, so that the interference modulation decreases.

 

Fig. 4 Reflection spectra of a 520 nm thick a-Si layer on a glass substrate at seven different temperatures. Measured points are connected for clarity.

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The results of two samples with amorphous silicon layers 520 and 480 nm thick were averaged. These averaged parameters were used for calculations of the temperature dependent absorption of diode laser radiation during laser heating for crystallization.

The temperature dependent spectra near the wavelength of 808 nm were fitted by just multiplying the values at room temperature by a thermal factor. In a wavelength range of ± 30 nm around 808 nm this factor proved to be independent of the wavelength. Figure 5 shows the measured reflectivity together with the fitted spectra at 20 °C, 270 °C, and 540 °C.

 

Fig. 5 Reflectivity of an a-Si film on borosilicate glass as depending on wavelength at different temperatures (20 °C blue, solid, 270 °C green, dotted, 540 °C red, dashed).The interesting wavelength of 808 nm is marked. Dots are measured values, lines are calculated from the model.

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In agreement with published measurements [9,16] the temperature dependence of n proved to be linear and that of k to be exponential according to

n(T)=n0+cn(TTR)2n0k(T)=k0eck(TTR)
with material parameters Cn and Ck
Cn=(4.0±0.2).103K1Ck=(3.0±0.3).103K1
and n0 and k0 the values at room temperature (TR = 20 °C). The resulting values for n(T) and k(T) are shown in Fig. 6 together with estimated accuracy limits.

 

Fig. 6 Temperature dependence of the refractive index n and the extinction coefficient k of a-Si deposited by electron beam evaporation for the wavelength 808 nm in the temperature range 20 °C to 1100 °C as calculated from the model. The dotted curves show the accuracy limits.

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For heating and crystallization of thin amorphous silicon layers on a glass substrate by a diode laser emitting at 808 nm, it is very useful to calculate the absorption as depending on the layer thickness, since there is a severe interference modulated absorption particularly at small thicknesses of the silicon layer (see Fig. 7 ). For these calculations the same optical model can be used as in the case of the determination of n and k because the bandwidth of the high power diode laser at 808 nm matches the requirements of the “thin layer on thick substrate” model and is similar to that of the fs-laser used for measurements. An additional interference modulation during heating due to the glass substrate does not occur due to the laser bandwidth.

 

Fig. 7 Calculated absorption of an a-Si layer on a glass substrate as depending on the layer thickness at 20 °C (blue, solid), 600 °C (red, dashed), and 1000 °C (black, dash-dotted). Inaccuracies limits due to that of n(T) and k(T) dotted.

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Convenient absorption values of a layer to be laser crystallized should be not too low, e.g. in the range above 20%. If the absorption is too low the required laser power for melting is rather high and the probability of damaging the thin layer is strongly enhanced, particularly due to strong absorption at defects in the film. Figure 7 clearly shows that high enough absorption (>20%) of the 808 nm diode laser radiation is achieved at room temperature for layers at least 400 nm thick. When the substrate is preheated to 600 °C, the absorption can be increased by a factor of about 4, and the minimum layer thickness reduces to 80 nm, however only for a small thickness range of about 50 nm. When choosing a useful layer thickness, interference effects within the layers need to be taken account of. However, for an experimental confirmation if this result further effects have to be taken account of. Particularly one has to choose a suitable buffer layer between glass and silicon which is well wetted by liquid silicon so that dewetting during the melting time is avoided which would lead to silicon droplets instead of a continuous layer.

4. Conclusions

The temperature dependent optical parameters n and k of thin a-Si films have be determined at the wavelength of 808 nm, important for large area low cost crystallization by diode lasers. This was achieved by measuring the reflectivity of a fs-laser beam used as a light source, for which the coherence length is in an appropriate range. From these results the absorption of a-Si for the diode laser wavelength was determined as depending on temperature and film thickness. If the substrate is heated to about 600 °C, endured by the substrate glass, and by making use of interference effects in the layer, the absorption can be increased by a factor of 4. It should be possible to crystallize a-Si layers 80 to 100 nm in thickness, useful for TFTs or seed layers for solar cells, by cw diode lasers emitting a wavelength of 808 nm.

References and links

1. F. Falk and G. Andrä, Solar Cells—Thin-Film Technologies (Intech 2011), Chap. 7: “Crystalline silicon thin film solar cells,” http://www.intechopen.com/books/solar-cells-thin-film-technologies.

2. G. Andrä, T. Gimpel, A. Gawlik, E. Ose, A. Bochmann, S. Christiansen, G. Sáfrán, J. L. Lábár, and F. Falk, “Epitaxial growth of silicon thin films for solar cells,” in Proc. 23rd European Photovoltaic Solar Energy Conf. (WIP, Munich, 2008), pp. 2194–2198.

3. G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films 511–512, 533–542 (2006). [CrossRef]  

4. P. I. Widenborg, A. Straub, and A. G. Aberle, “Epitaxial thickening of AIC poly-Si seed layers on glass by solid phase epitaxy,” J. Cryst. Growth 276(1-2), 19–28 (2005). [CrossRef]  

5. A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids 338–340, 758–761 (2004). [CrossRef]  

6. G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C 5, 3221–3223 (2008).

7. M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett. 97(3), 032102 (2010). [CrossRef]  

8. N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc. 5, 109–117 (2010). [CrossRef]  

9. J. D. Hoyland and D. Sands, “Temperature dependent refractive index of amorphous silicon determined by time-resolved reflectivity during low fluence excimer laser heating,” J. Appl. Phys. 99(6), 063516 (2006). [CrossRef]  

10. G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett. 67(1), 229–232 (2012). [CrossRef]  

11. G. Andrä, J. Bergmann, A. Gawlik, J. Plentz, I. Höger, T. Schmidt, and F. Falk, “Thin film solar cells based on diode laser crystallized polycrystalline silicon,” in Proc. 26th Europ. Photovoltaic Solar Energy Conf. (WIP Munich 2011), pp. 2803–2806.

12. X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films 519(1), 58–63 (2010). [CrossRef]  

13. B. K. Sun, X. Zhang, and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Trans. 40(7), 1591–1600 (1997). [CrossRef]  

14. O. Stenzel, The Physics of Thin Film Optical Spectra (Springer, 2005), p. 116ff.

15. G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C: Solid State 10(3), 467–477 (1977). [CrossRef]  

16. G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett. 66(26), 3570–3572 (1995). [CrossRef]  

References

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  1. F. Falk and G. Andrä, Solar Cells—Thin-Film Technologies (Intech 2011), Chap. 7: “Crystalline silicon thin film solar cells,” http://www.intechopen.com/books/solar-cells-thin-film-technologies .
  2. G. Andrä, T. Gimpel, A. Gawlik, E. Ose, A. Bochmann, S. Christiansen, G. Sáfrán, J. L. Lábár, and F. Falk, “Epitaxial growth of silicon thin films for solar cells,” in Proc. 23rd European Photovoltaic Solar Energy Conf. (WIP, Munich, 2008), pp. 2194–2198.
  3. G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
    [CrossRef]
  4. P. I. Widenborg, A. Straub, and A. G. Aberle, “Epitaxial thickening of AIC poly-Si seed layers on glass by solid phase epitaxy,” J. Cryst. Growth276(1-2), 19–28 (2005).
    [CrossRef]
  5. A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
    [CrossRef]
  6. G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5, 3221–3223 (2008).
  7. M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
    [CrossRef]
  8. N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
    [CrossRef]
  9. J. D. Hoyland and D. Sands, “Temperature dependent refractive index of amorphous silicon determined by time-resolved reflectivity during low fluence excimer laser heating,” J. Appl. Phys.99(6), 063516 (2006).
    [CrossRef]
  10. G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
    [CrossRef]
  11. G. Andrä, J. Bergmann, A. Gawlik, J. Plentz, I. Höger, T. Schmidt, and F. Falk, “Thin film solar cells based on diode laser crystallized polycrystalline silicon,” in Proc. 26th Europ. Photovoltaic Solar Energy Conf. (WIP Munich 2011), pp. 2803–2806.
  12. X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
    [CrossRef]
  13. B. K. Sun, X. Zhang, and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Trans.40(7), 1591–1600 (1997).
    [CrossRef]
  14. O. Stenzel, The Physics of Thin Film Optical Spectra (Springer, 2005), p. 116ff.
  15. G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C: Solid State10(3), 467–477 (1977).
    [CrossRef]
  16. G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett.66(26), 3570–3572 (1995).
    [CrossRef]

2012

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

2010

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

2008

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5, 3221–3223 (2008).

2006

J. D. Hoyland and D. Sands, “Temperature dependent refractive index of amorphous silicon determined by time-resolved reflectivity during low fluence excimer laser heating,” J. Appl. Phys.99(6), 063516 (2006).
[CrossRef]

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

2005

P. I. Widenborg, A. Straub, and A. G. Aberle, “Epitaxial thickening of AIC poly-Si seed layers on glass by solid phase epitaxy,” J. Cryst. Growth276(1-2), 19–28 (2005).
[CrossRef]

2004

A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
[CrossRef]

1997

B. K. Sun, X. Zhang, and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Trans.40(7), 1591–1600 (1997).
[CrossRef]

1995

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett.66(26), 3570–3572 (1995).
[CrossRef]

1977

G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C: Solid State10(3), 467–477 (1977).
[CrossRef]

Aberle, A. G.

P. I. Widenborg, A. Straub, and A. G. Aberle, “Epitaxial thickening of AIC poly-Si seed layers on glass by solid phase epitaxy,” J. Cryst. Growth276(1-2), 19–28 (2005).
[CrossRef]

Andrä, G.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5, 3221–3223 (2008).

A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
[CrossRef]

Baettig, R.

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

Beaucarne, G.

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

Bergmann, J.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
[CrossRef]

Bochmann, A.

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

Browning, N. D.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Brunner, R.

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

Christiansen, S.

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

Duerinckx, F.

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

Evans, J. E.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Falk, F.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5, 3221–3223 (2008).

A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
[CrossRef]

Gawlik, A.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

Ghosh, G.

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett.66(26), 3570–3572 (1995).
[CrossRef]

Grigoropoulos, C. P.

B. K. Sun, X. Zhang, and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Trans.40(7), 1591–1600 (1997).
[CrossRef]

Höger, I.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

Hoyland, J. D.

J. D. Hoyland and D. Sands, “Temperature dependent refractive index of amorphous silicon determined by time-resolved reflectivity during low fluence excimer laser heating,” J. Appl. Phys.99(6), 063516 (2006).
[CrossRef]

Kim, H. J.

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

Kuzma, I.

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

LaGrange, T.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Lichtenstein, N.

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

Lu, J. P.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Maeder, X.

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

Mayer, G.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

McGowan, S.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Michler, J.

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

Mohammed-Brahim, T.

A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
[CrossRef]

Müller, J.

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

Niederberger, C.

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

Nikolova, L.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Poortmans, J.

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

Rosei, F.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Saboundji, A.

A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
[CrossRef]

Sands, D.

J. D. Hoyland and D. Sands, “Temperature dependent refractive index of amorphous silicon determined by time-resolved reflectivity during low fluence excimer laser heating,” J. Appl. Phys.99(6), 063516 (2006).
[CrossRef]

Schmidl, G.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

Sill, I.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

Siwick, B. J.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Steglich, M.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

Straub, A.

P. I. Widenborg, A. Straub, and A. G. Aberle, “Epitaxial thickening of AIC poly-Si seed layers on glass by solid phase epitaxy,” J. Cryst. Growth276(1-2), 19–28 (2005).
[CrossRef]

Sun, B. K.

B. K. Sun, X. Zhang, and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Trans.40(7), 1591–1600 (1997).
[CrossRef]

Taheri, M. L.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Teslich, N.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

Thutupalli, G. K. M.

G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C: Solid State10(3), 467–477 (1977).
[CrossRef]

Tomlin, S. G.

G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C: Solid State10(3), 467–477 (1977).
[CrossRef]

Valk, B.

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

Van Nieuwenhuysen, K.

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

Widenborg, P. I.

P. I. Widenborg, A. Straub, and A. G. Aberle, “Epitaxial thickening of AIC poly-Si seed layers on glass by solid phase epitaxy,” J. Cryst. Growth276(1-2), 19–28 (2005).
[CrossRef]

Zhang, X.

B. K. Sun, X. Zhang, and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Trans.40(7), 1591–1600 (1997).
[CrossRef]

Appl. Phys. Lett.

M. L. Taheri, S. McGowan, L. Nikolova, J. E. Evans, N. Teslich, J. P. Lu, T. LaGrange, F. Rosei, B. J. Siwick, and N. D. Browning, “In situ laser crystallization of amorphous silicon: controlled nanosecond studies in the dynamic transmission electron microscope,” Appl. Phys. Lett.97(3), 032102 (2010).
[CrossRef]

G. Ghosh, “Temperature dispersion of refractive indices in crystalline and amorphous silicon,” Appl. Phys. Lett.66(26), 3570–3572 (1995).
[CrossRef]

Int. J. Heat Mass Trans.

B. K. Sun, X. Zhang, and C. P. Grigoropoulos, “Spectral optical function of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Trans.40(7), 1591–1600 (1997).
[CrossRef]

J. Appl. Phys.

J. D. Hoyland and D. Sands, “Temperature dependent refractive index of amorphous silicon determined by time-resolved reflectivity during low fluence excimer laser heating,” J. Appl. Phys.99(6), 063516 (2006).
[CrossRef]

J. Cryst. Growth

P. I. Widenborg, A. Straub, and A. G. Aberle, “Epitaxial thickening of AIC poly-Si seed layers on glass by solid phase epitaxy,” J. Cryst. Growth276(1-2), 19–28 (2005).
[CrossRef]

J. Non-Cryst. Solids

A. Saboundji, T. Mohammed-Brahim, G. Andrä, J. Bergmann, and F. Falk, “Thin film transistors on large single crystalline regions of silicon induced by cw laser crystallization,” J. Non-Cryst. Solids338–340, 758–761 (2004).
[CrossRef]

J. Phys. C: Solid State

G. K. M. Thutupalli and S. G. Tomlin, “The optical properties of amorphous and crystalline silicon,” J. Phys. C: Solid State10(3), 467–477 (1977).
[CrossRef]

Mater. Lett.

G. Schmidl, G. Andrä, J. Bergmann, A. Gawlik, I. Höger, I. Sill, M. Steglich, F. Falk, and G. Mayer, “Sputtered amorphous silicon thin films for diode laser crystallization,” Mater. Lett.67(1), 229–232 (2012).
[CrossRef]

Phys. Proc.

N. Lichtenstein, R. Baettig, R. Brunner, J. Müller, B. Valk, A. Gawlik, J. Bergmann, and F. Falk, “Scalable, high power line focus diode laser for crystallizing of silicon thin films,” Phys. Proc.5, 109–117 (2010).
[CrossRef]

Phys. Status Solidi C

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5, 3221–3223 (2008).

Thin Solid Films

G. Beaucarne, F. Duerinckx, I. Kuzma, K. Van Nieuwenhuysen, H. J. Kim, and J. Poortmans, “Epitaxial thin-film Si solar cells,” Thin Solid Films511–512, 533–542 (2006).
[CrossRef]

X. Maeder, C. Niederberger, S. Christiansen, A. Bochmann, G. Andrä, A. Gawlik, F. Falk, and J. Michler, “Microstructure and lattice bending in polycrystalline laser-crystallized silicon thin films for photovoltaic applications,” Thin Solid Films519(1), 58–63 (2010).
[CrossRef]

Other

O. Stenzel, The Physics of Thin Film Optical Spectra (Springer, 2005), p. 116ff.

F. Falk and G. Andrä, Solar Cells—Thin-Film Technologies (Intech 2011), Chap. 7: “Crystalline silicon thin film solar cells,” http://www.intechopen.com/books/solar-cells-thin-film-technologies .

G. Andrä, T. Gimpel, A. Gawlik, E. Ose, A. Bochmann, S. Christiansen, G. Sáfrán, J. L. Lábár, and F. Falk, “Epitaxial growth of silicon thin films for solar cells,” in Proc. 23rd European Photovoltaic Solar Energy Conf. (WIP, Munich, 2008), pp. 2194–2198.

G. Andrä, J. Bergmann, A. Gawlik, J. Plentz, I. Höger, T. Schmidt, and F. Falk, “Thin film solar cells based on diode laser crystallized polycrystalline silicon,” in Proc. 26th Europ. Photovoltaic Solar Energy Conf. (WIP Munich 2011), pp. 2803–2806.

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Figures (7)

Fig. 1
Fig. 1

Optical set-up for the measurement of temperature dependent reflectivity (see text).

Fig. 2
Fig. 2

Spectra of a 520 nm thick a-Si film measured by a spectrometer (dots mark every tenth of the measured wavelengths) and fitted spectra for reflection R (blue, dotted), transmission T (red, solid) and absorption A = 1-R-T (black, dash-dotted). The diameter of the points gives a good hint for the accuracy of measurement.

Fig. 3
Fig. 3

Dispersion of n and k of a-Si at room temperature.

Fig. 4
Fig. 4

Reflection spectra of a 520 nm thick a-Si layer on a glass substrate at seven different temperatures. Measured points are connected for clarity.

Fig. 5
Fig. 5

Reflectivity of an a-Si film on borosilicate glass as depending on wavelength at different temperatures (20 °C blue, solid, 270 °C green, dotted, 540 °C red, dashed).The interesting wavelength of 808 nm is marked. Dots are measured values, lines are calculated from the model.

Fig. 6
Fig. 6

Temperature dependence of the refractive index n and the extinction coefficient k of a-Si deposited by electron beam evaporation for the wavelength 808 nm in the temperature range 20 °C to 1100 °C as calculated from the model. The dotted curves show the accuracy limits.

Fig. 7
Fig. 7

Calculated absorption of an a-Si layer on a glass substrate as depending on the layer thickness at 20 °C (blue, solid), 600 °C (red, dashed), and 1000 °C (black, dash-dotted). Inaccuracies limits due to that of n(T) and k(T) dotted.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

n(λ)= a (λb) 2 +c k(λ)= d (λe) 2
a=155000n m 2 ,b=220nm,c=3.5,d=1180n m 2 ,e=610nm.
n(T)= n 0 + c n (T T R ) 2 n 0 k(T)= k 0 e c k (T T R )
C n =(4.0±0.2) .10 3 K 1 C k =(3.0±0.3).1 0 3 K 1

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